Research Journal of Applied Sciences, Engineering and Technology 10(6): 716-722, 2015
DOI:10.19026/rjaset.10.2482
ISSN: 2040-7459; e-ISSN: 2040-7467
© 2015 Maxwell Scientific Publication Corp.
Submitted: February 13, 2015
Accepted: March 1, 2015
Published: June 20, 2015
Research Article
Modelling the Effects of Leakage Current Resistance in Transmission Line
Saraa I. Khalel and M.F. Rahmat
Faculty of Electrical Engineering, Universiti Teknologi Malaysia, Johor 81110, Malaysia
Abstract: Determining the mechanisms and influences of leakage current resistance that results power loss in
transmission line is an outstanding quest. Perfect insulations are pre-requisite for electrical systems to achieve
maximum efficiency. The level of insulator contamination determines the loss enhancement in power transmission
systems mediated by leakage current. This phenomenon in turn changes the physical characteristics of the insulation
through the enhancement of resistance. In this study, we propose a new model using MATLAB to examine the
effect of leakage current resistance on the short and medium transmission lines of five buses. Three levels of leakage
resistance (high, medium and low) are incorporated into the model through delta-star/star-delta conversion and twoport network concept. The input impedances for the load flow equations are updated. Results show that the leakage
current resistance mediated via the deposition of the pollution on the transmission line plays a major role in the
power loss. The amount of power losses and the cost factor in the presence of leakage can be estimated with this
model our simplified model to examine the effects of leakage current in power transmission lines may be useful for
loss minimization and remedy.
Keywords: Insulator, leakage current, modelling, transmission line
leakage currents originate non-uniform heating on the
surface of the insulator and this in turn causes dry- band
arcing and possible flashover. Insulation flashover leads
to service outages, which affect reliability and results
economic losses for both the user and the supply
company. The transmission systems are expensive and
damages in their insulation often causes high economic
losses and life-threatening effects. Therefore, an in
depth examination of leakage current is significant for
all electrical devices and insulators (Jiang et al., 2011;
Fierro-Chavez et al., 1996; Piah and Darus, 2004).
Overcoming these leakage effects and minimizing the
losses involved are the challenging tasks.
The leakage current both for devices and for
insulators is drawn from the main supply. it never
contributes to any useful power in the load and instead
leads to wastage. Nevertheless, it remains important in
the design, selection and installation of the transmission
line. The performance of the insulator is drastically
affected by the increase in leakage current. In this
situation, the current cannot pass inside the insulator
and a path of relatively low resistance exists over the
surface, as shown in Fig. 1 (Amin et al., 2009).
The leakage current is found to directly
proportional to the surface pollution deposit. In fact,
thick layers of pollutants are capable of trapping more
rain water in wet conditions. Much water on the surface
reduces the surface resistance and thereby enhances the
leakage current. The insulators used in coastal and
INTRODUCTION
Leakage current is defined as any current that
flows from the hot conductor to the ground over the
outside surface of an insulator. In the absence of a
grounding connection, this current flow from the
conductive part or the surface of non-conductive parts
to ground if a conductive path is available and it often
become fatal when touched by humans. Detecting,
monitoring, quantifying and determining this leakage
current are essential for maintaining safety and ensuring
cost efficiency (Amin et al., 2009). High power
transmission line can be protected via the detection of
leakage current resistance and assessment of the
conduction quality during operation. The working
efficiency of the transmission system depends on the
leakage strength. The value of total resistance between
point of insulation failure and the ground is a significant
factor in ensuring safety.
The insulator in transmission line plays a key role
in the power system. Generally, the insulation in any
transmission system deteriorates over a particular time
span because of temperature, moisture and other
factors. Based on the nature of the material used,
insulators can be categorized as porcelain, glass and
polymer insulators. These insulators in transmission
lines under operation are frequently exposed to
pollution effects that accumulate on their surfaces.
Consequently, under wet conditions, the generated
Corresponding Author: Saraa I. Khalel, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, Johor 81110,
Malaysia
This work is licensed under a Creative Commons Attribution 4.0 International License (URL: http://creativecommons.org/licenses/by/4.0/).
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Res. J. Appl. Sci. Eng. Technol., 10(6): 716-722, 2015
VS
V
R
Fig. 2: Two-port representation of transmission line
deposits on the insulators in transmission lines give rise
to the leakage current. The Majority of previous works
on the load flow in power systems neglected the role of
leakage currents compared with that of the actual
current flown in the transmission line (Wadhwa, 2005).
However, in our view, the influences of leakage
currents must be considered in the load
flowthrough representation of all towers as a resistance.
The purposes are to make an accurate estimate of loss
and identify the corresponding solution needed. A
complete evaluation of this leakage current related loss
in transmission line may assist the power provider to
save on power costs and ensure the smooth running of
power station at this juncture when the fuel cost is
exponentially increasing. Generally, leakage current
appears in every transmission line as low, medium and
high levels. We focus on the short and medium
transmission line model.
Fig. 1: Low resistance path on the insulator surface
industrial environments receive severe pollution
deposits. In service, the surface resistance of the
insulator under wet conditions the presence of
contaminations considerably decreases (Piah and Darus,
2004). Essentially, the insulator with a surface
resistance lower than 400 kΩ must be replaced or
washed off to avoid the leakage current losses (FierroChavez et al., 1996). The power loss is obviously low
in the absence of any precipitation (Wei et al., 2012).
Despite some efforts, no standard method has been
established thus far to determine the amount of leakage
currents or compute the effective leakage current losses
in terms power and economy.
We developed an improved transmission line
model to determine the effect of surface insulator
resistance on the load flow program for the system. The
values of active and reactive power components,
voltages and angles for buses are calculated. The effects
of leakage current on the real power losses, especially
with the increase in fuel cost, are evaluated. The
medium and short transmission lines (five buses) are
used with high, medium and low levels of leakage
resistance. Delta-star/star-delta conversion and two-port
network concept are utilized to update the input
impedances for the load flow equations. The effects of
these losses because of leakage over a long period of
the time are analysed. This model may be useful in
identifying the insulator severity level in load flow
studies and determine loss in transmission line.
Short transmission line model: Resistance, inductance
and capacitance are the integrated components of any
transmission line. For short transmission lines (lower
than 80 km), the capacitance (c) can be neglected and
the equivalent circuit includes only the Resistance (R)
and the inductance (XL) (Saadat, 2002). We use a series
connected model with a Voltage source (VS), current
source (IS) and Voltage load (VR) to characterize the
short and medium transmission line as depicted in
Fig. 2. The line containing the impedance is divided
into many sections during the incorporation of the
effects of leakage current resistance in the transmission
line between buses. All sections are represented
following π-section and two-port network concept.
The current voltage relationship in the two-port
network is written as:
METHODOLOGY
Modeling: Transmission lines are specialized cables or
conducting structures designed to carry electricity or
the electrical signal of radio frequency. They are used
for electric-power transmission (bulk transfer
of electrical energy) from generating power plants to
the electrical substations. The interconnected
transmission lines are called transmission networks. As
one of the most important and integrated parts of
electric power systems, transmission lines require
absolute stabilization, precise control and regular
monitoring. As previously mentioned, the pollution
V = AV + BI
(1)
V
AB V
= I
C D I
(3)
I = CV + DI
717
A=1
B=Z
C=0
D=A
(2)
(4)
Res. J. Appl. Sci. Eng. Technol., 10(6): 716-722, 2015
Fig. 3: Short transmission line with leakage current effects
be modelled as nominal π and Т forms. In this study, πrepresentation is used, where the total admittance as a
result of the line capacitance is equally divided into two
halves and each half is connected at both transmitter
and receiver ends (Saadat, 2002). The impedance
equation yields:
(a)
Y = ,G + jw0 1 l
(b)
where, C is the line to neutral capacitance per km, Y is
the total shunt admittance, l is the line length and w0 is
the signal frequency. Under normal condition, the shunt
conductance per unit length represents the leakage
current over the insulator. The leakage current as a
result of the corona is negligible and the value of G is
assumed to be zero. Using Fig. 5, the transmitter end
voltage and current for the nominal π-section are
obtained.
The constants A, B, C and D for the nominal π
model take the form:
Fig. 4: Delta (a) star (b) conversion in short transmission line
The number of towers N existing in the
transmission line is defined by:
N = T / d
(5)
where,
T = The total distance between two buses
d = The distance between two towers
Figure 3 shows that a new network model can be
designed by introduction of leakage current resistance
in the transmission line.
This new model contains the delta-star/star-delta
conversion as displayed in Fig. 4, which is used to
simplify the two-port network.
The expressions for the impedances (Z1, Z2 and
Z3) in the simplified two-port net work model are
obtained as:
=
' =
( =
∗"#$
%"#$ %"#&
∗"#&
%"#$ %"#&
"#$ ∗"#&
%"#$ %"#&
(9)
A = 1 + Z
C = Y 1 +
3
'
53
6
,B = Z
, D = 1 +
(10)
53
'
(11)
Generally, the constants A, B, C and D are
complex. the π model is a symmetrical two-port
network model, so A = D is obtained. The determinant
of the transmission matrix represented by Eq. (3) is
reduced to:
(6)
AD − BC = 1
(7)
(12)
In solving Eq. (3), the quantities in the receiver end
in terms of the transmitter one can be expressed as:
(8)
where,
Z
= The impedance line
R * and R *' = Leakage current resistances
D − B v:
V
=
I
– C A I:
(13)
Now, the new model for medium transmission line
in the presence of leakage current resistance (Fig. 6) is
achieved.
The values of the transmission matrix for all
sections (A, B, C and D) can be computed in the
presence of leakage effects. The number of sections
Medium transmission line model: Transmission lines
of length longer than 80 km and shorter than 250 km
are classified as medium transmission lines. They can
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Res. J. Appl. Sci. Eng. Technol., 10(6): 716-722, 2015
Fig. 5: Nominal π-model for medium length line
Fig. 6: Medium transmission line modelled with leakage current resistance
(c)
(d)
Fig. 7: Delta (c) star (d) conversion in medium transmission line
Z =
critically depends on the line. Finally, the expression
for transmission matrix is represented as:
A B
A B
A B
∗ ' ' ∗ ( (
C D
C ' D'
C ( D(
A > B>
A = B=
=
…...
C = D=
C > D>
Z' =
(14)
Z( =
The model network as displayed in Fig. 7 encloses
the delta-star/star-delta conversion which simplifies the
two-port network concept.
The impedance equations in this simplified picture
are given by:
Zin =
Zin' =
$
A B C∗"#$
&∗
$
A B C%"#$
&∗
$
A B C∗"#&
&∗
$
A B C∗"#&
&∗
D
E ∗5FG$
D
%5FG$ %5FG&
E
D
E ∗5FG&
D
%5FG$ %5FG&
E
5FG$ ∗5FG&
D
%5FG$ %5FG&
E
(17)
(18)
(19)
The input impedance in the load flow equation is
updated to include the leakage current resistance.
RESULTS AND DISCUSSION
Table 1 displays the impedance and admittance
between two buses in the 5-bus system without the
effect of leakage current resistance (Stevenson, 1982).
Table 2 lists the corresponding values in the presence of
leakage current resistance effects (400 kΩ) in all
transmission lines.
Figure 8 and 9 shows the variation of impedance
and admittance for short transmission line between
(15)
(16)
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Res. J. Appl. Sci. Eng. Technol., 10(6): 716-722, 2015
Table 1: Data for 5-bus system
Impedance without leakage current effect
------------------------------------------------------------------------------------------------------------------------------------------Length km
R per unit
X per unit
Y/2
Line bus to bus
1-2
64.4
0.0420
0.168
0
1-3
48.3
0.0314
0.126
0
2-5
48.3
0.0314
0.126
0
3-4
96.5
0.0630
0.252
0+j0.0305058
5-4
128.7
0.0840
0.336
0+j0.0410078
3-5
80.5
0.0530
0.210
0+j0.0255048
Table 2: Data for 5-bus system
Impedance with leakage current effect
------------------------------------------------------------------------------------------------------------------------------------------Length km
R per unit
X per unit
Y/2
Line bus to bus
1-2
64.4
0.0417
0.1685
0.0368
1-3
48.3
0.0312
0.1269
0.0288
2-5
48.3
0.0312
0.1269
0.0288
3-4
96.5
0.0619
0.2532
0.0513+j0.0304
5-4
128.7
0.0814
0.3382
0.0682+j0.0409
3-5
80.5
0.0520
0.2112
0.0429+j0.0254
Fig. 8: Impedance for short transmission line between buses 1-2
Fig. 9: Admittance for short transmission line between buses 1-2
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Res. J. Appl. Sci. Eng. Technol., 10(6): 716-722, 2015
Fig. 10: Impedance for medium transmission line between buses 3-4
Fig. 11: Admittance for medium transmission line between buses 3-4
buses 1-2 in the presence of the effect of leakage
current resistance. The leakage current resistance value
is varied between 0.4-7 M Ω.
Figure 8 and 9 clearly exhibit that for increased
value leakage current resistance both the impedance
and admittance is increased. However, by lowering
value the leakage current resistance the impedance is
found to be decreased and admittance is increased.
Only the real part (resistance) of the admittance is
shown with the effect leakage current resistance.
Figure 10 and 11 reveal that for higher effect of
leakage current resistance, the impedance is lower and
the admittance is higher. However, as the value leakage
current resistance is reduced the impedance is found to
decrease and admittance is increased. The real part and
imaginary part of the admittance are shown with the
effect leakage current resistance.
CONCLUSION
The design of the newly developed model for short
and medium transmission line are presented to establish
the relationship between effect of leakage current and
load flow in the system. Each tower in the transmission
line is represented as a resistance to accurately estimate
of loss. The leakage resistance is incorporated into the
model through delta-star/star-delta conversion and twoport network concept to update the load flow equations.
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Res. J. Appl. Sci. Eng. Technol., 10(6): 716-722, 2015
Three levels of leakage current such as high, medium
and low resistances are used. MATLAB programming
is used to model the transmission lines with 5-buses. It
is asserted that the leakage current resistance
significantly contributes towards the power loss. The
impedances and admittances between different buses
are found to vary strongly with the leakage current
resistance. Our comprehensive model, including the
effects of leakage current in power transmission lines
may serve to achieve an insight in loss minimization,
control and safety.
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Stevenson, W.D., 1982. Elements of Power System
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